Abstract

We present a theoretical analysis of the properties of an unseeded optical parametic amplifier (OPA) used as the source of entangled photons for applications in quantum lithography. We first study the dependence of the excitation rate of a two-photon absorber on the intensity of the light leaving the OPA. We find that the rate depends linearly on intensity only for output beams so weak that they contain fewer than one photon per mode. We also study the use of an N-photon absorber for arbitrary N as the recording medium to be used with such a light source. We find that the contrast of the interference pattern and the sharpness of the fringe maxima tend to increase with increasing values of N, but that the density of fringes and thus the limiting resolution does not increase with N. We conclude that the output of an unseeded OPA exciting an N-photon absorber provides an attractive system in which to perform quantum lithography.

© 2007 Optical Society of America

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  1. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
    [CrossRef] [PubMed]
  2. M. D'Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
    [CrossRef] [PubMed]
  3. S. J. Bentley and R. W. Boyd, "Nonlinear optical lithography with ultra-high sub-Rayleigh resolution," Opt. Express 12, 5735-5740 (2004).
    [CrossRef] [PubMed]
  4. R. W. Boyd and S. J. Bentley, "Recent progress in quantum and nonlinear optical lithography," J. Mod. Opt. 53, 713-718 (2006).
    [CrossRef]
  5. G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, "Comment on 'Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,"' Phys. Rev. Lett. 86, 1389-1389 (2001).
    [CrossRef] [PubMed]
  6. E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers," Phys. Rev. A 64, 043802 (2001).
    [CrossRef]
  7. E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Parametric downconversion vs optical parametric amplification: a comparison of their quantum statistics," J. Mod. Opt. 49, 529-537 (2002).
    [CrossRef]
  8. J. Gea-Banacloche, "Two-photon absorption of nonclassical light," Phys. Rev. Lett. 62, 1603-1606 (1989).
    [CrossRef] [PubMed]
  9. J. Javanainen and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
    [CrossRef] [PubMed]
  10. J. Perina, B. E. A. Saleh, and M. C. Teich, "Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state," Phys. Rev. A 57, 3972-3986 (1998).
    [CrossRef]
  11. N. P. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
    [CrossRef] [PubMed]
  12. B. Dayan, A. Peer, A. A. Friesem, and Y. Silberberg, "Nonlinear interactions with an ultrahigh flux of broadband entangled photons," Phys. Rev. Lett. 94, 043602 (2005).
    [CrossRef] [PubMed]
  13. C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
    [CrossRef] [PubMed]
  14. J. K. Ranka, A. L. Gaeta, A. Baltuska, M. Pshenichnikov, and D. A. Wiersma, "Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode," Opt. Lett. 22, 1344-1346 (1997).
    [CrossRef]
  15. P. S. Westbrook, S. Wielandy, and M. Fishteyn, "Two-photon fourth-order polarimetery," Opt. Lett. 30, 655-657 (2005).
    [CrossRef] [PubMed]
  16. J. M. Roth, T. E. Murphy, and C. Xu, "Ultrasensitive and high-dynamic-range two-photon absorption in a GaAs photomultiplier tube," Opt. Lett. 27, 2076-2078 (2002).
    [CrossRef]
  17. E. Yablonovitch and R. B. Vrijen, "Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure," Opt. Eng. 38, 334-338 (1999).
    [CrossRef]
  18. D. V. Korobkin and E. Yablonovitch, "Two-fold spatial resolution enhancement by two-photon exposure of photographic film," Opt. Eng. 41, 1729-17322002).
    [CrossRef]
  19. H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, "Implementation of sub-Rayleigh lithography using an N-photon absorber," J. Mod. Opt. 53, 2271-2277 (2006).
    [CrossRef]

2006 (2)

R. W. Boyd and S. J. Bentley, "Recent progress in quantum and nonlinear optical lithography," J. Mod. Opt. 53, 713-718 (2006).
[CrossRef]

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, "Implementation of sub-Rayleigh lithography using an N-photon absorber," J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

2005 (2)

B. Dayan, A. Peer, A. A. Friesem, and Y. Silberberg, "Nonlinear interactions with an ultrahigh flux of broadband entangled photons," Phys. Rev. Lett. 94, 043602 (2005).
[CrossRef] [PubMed]

P. S. Westbrook, S. Wielandy, and M. Fishteyn, "Two-photon fourth-order polarimetery," Opt. Lett. 30, 655-657 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (3)

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Parametric downconversion vs optical parametric amplification: a comparison of their quantum statistics," J. Mod. Opt. 49, 529-537 (2002).
[CrossRef]

J. M. Roth, T. E. Murphy, and C. Xu, "Ultrasensitive and high-dynamic-range two-photon absorption in a GaAs photomultiplier tube," Opt. Lett. 27, 2076-2078 (2002).
[CrossRef]

D. V. Korobkin and E. Yablonovitch, "Two-fold spatial resolution enhancement by two-photon exposure of photographic film," Opt. Eng. 41, 1729-17322002).
[CrossRef]

2001 (3)

G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, "Comment on 'Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,"' Phys. Rev. Lett. 86, 1389-1389 (2001).
[CrossRef] [PubMed]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers," Phys. Rev. A 64, 043802 (2001).
[CrossRef]

M. D'Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

2000 (1)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

1999 (1)

E. Yablonovitch and R. B. Vrijen, "Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure," Opt. Eng. 38, 334-338 (1999).
[CrossRef]

1998 (1)

J. Perina, B. E. A. Saleh, and M. C. Teich, "Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state," Phys. Rev. A 57, 3972-3986 (1998).
[CrossRef]

1997 (1)

1995 (1)

N. P. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

1990 (1)

J. Javanainen and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
[CrossRef] [PubMed]

1989 (1)

J. Gea-Banacloche, "Two-photon absorption of nonclassical light," Phys. Rev. Lett. 62, 1603-1606 (1989).
[CrossRef] [PubMed]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Agarwal, G. S.

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Parametric downconversion vs optical parametric amplification: a comparison of their quantum statistics," J. Mod. Opt. 49, 529-537 (2002).
[CrossRef]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers," Phys. Rev. A 64, 043802 (2001).
[CrossRef]

G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, "Comment on 'Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,"' Phys. Rev. Lett. 86, 1389-1389 (2001).
[CrossRef] [PubMed]

Baltuska, A.

Bentley, S. J.

R. W. Boyd and S. J. Bentley, "Recent progress in quantum and nonlinear optical lithography," J. Mod. Opt. 53, 713-718 (2006).
[CrossRef]

S. J. Bentley and R. W. Boyd, "Nonlinear optical lithography with ultra-high sub-Rayleigh resolution," Opt. Express 12, 5735-5740 (2004).
[CrossRef] [PubMed]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Parametric downconversion vs optical parametric amplification: a comparison of their quantum statistics," J. Mod. Opt. 49, 529-537 (2002).
[CrossRef]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers," Phys. Rev. A 64, 043802 (2001).
[CrossRef]

G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, "Comment on 'Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,"' Phys. Rev. Lett. 86, 1389-1389 (2001).
[CrossRef] [PubMed]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd and S. J. Bentley, "Recent progress in quantum and nonlinear optical lithography," J. Mod. Opt. 53, 713-718 (2006).
[CrossRef]

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, "Implementation of sub-Rayleigh lithography using an N-photon absorber," J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

S. J. Bentley and R. W. Boyd, "Nonlinear optical lithography with ultra-high sub-Rayleigh resolution," Opt. Express 12, 5735-5740 (2004).
[CrossRef] [PubMed]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Parametric downconversion vs optical parametric amplification: a comparison of their quantum statistics," J. Mod. Opt. 49, 529-537 (2002).
[CrossRef]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers," Phys. Rev. A 64, 043802 (2001).
[CrossRef]

G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, "Comment on 'Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,"' Phys. Rev. Lett. 86, 1389-1389 (2001).
[CrossRef] [PubMed]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Chang, H. J.

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, "Implementation of sub-Rayleigh lithography using an N-photon absorber," J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

Chekhova, M. V.

M. D'Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

D'Angelo, M.

M. D'Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Dayan, B.

B. Dayan, A. Peer, A. A. Friesem, and Y. Silberberg, "Nonlinear interactions with an ultrahigh flux of broadband entangled photons," Phys. Rev. Lett. 94, 043602 (2005).
[CrossRef] [PubMed]

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Edamatsu, K.

N. P. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Fishteyn, M.

Friesem, A. A.

B. Dayan, A. Peer, A. A. Friesem, and Y. Silberberg, "Nonlinear interactions with an ultrahigh flux of broadband entangled photons," Phys. Rev. Lett. 94, 043602 (2005).
[CrossRef] [PubMed]

Gaeta, A. L.

Gea-Banacloche, J.

J. Gea-Banacloche, "Two-photon absorption of nonclassical light," Phys. Rev. Lett. 62, 1603-1606 (1989).
[CrossRef] [PubMed]

Georgiades, N. P.

N. P. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Gould, P. L.

J. Javanainen and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
[CrossRef] [PubMed]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Javanainen, J.

J. Javanainen and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
[CrossRef] [PubMed]

Kimble, H. J.

N. P. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Korobkin, D. V.

D. V. Korobkin and E. Yablonovitch, "Two-fold spatial resolution enhancement by two-photon exposure of photographic film," Opt. Eng. 41, 1729-17322002).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Murphy, T. E.

Nagasako, E. M.

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Parametric downconversion vs optical parametric amplification: a comparison of their quantum statistics," J. Mod. Opt. 49, 529-537 (2002).
[CrossRef]

G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, "Comment on 'Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,"' Phys. Rev. Lett. 86, 1389-1389 (2001).
[CrossRef] [PubMed]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers," Phys. Rev. A 64, 043802 (2001).
[CrossRef]

O'Sullivan-Hale, M. N.

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, "Implementation of sub-Rayleigh lithography using an N-photon absorber," J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Peer, A.

B. Dayan, A. Peer, A. A. Friesem, and Y. Silberberg, "Nonlinear interactions with an ultrahigh flux of broadband entangled photons," Phys. Rev. Lett. 94, 043602 (2005).
[CrossRef] [PubMed]

Perina, J.

J. Perina, B. E. A. Saleh, and M. C. Teich, "Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state," Phys. Rev. A 57, 3972-3986 (1998).
[CrossRef]

Polzik, E. S.

N. P. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

Pshenichnikov, M.

Ranka, J. K.

Roth, J. M.

Saleh, B. E. A.

J. Perina, B. E. A. Saleh, and M. C. Teich, "Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state," Phys. Rev. A 57, 3972-3986 (1998).
[CrossRef]

Shih, Y.

M. D'Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Shin, H.

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, "Implementation of sub-Rayleigh lithography using an N-photon absorber," J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

Silberberg, Y.

B. Dayan, A. Peer, A. A. Friesem, and Y. Silberberg, "Nonlinear interactions with an ultrahigh flux of broadband entangled photons," Phys. Rev. Lett. 94, 043602 (2005).
[CrossRef] [PubMed]

Teich, M. C.

J. Perina, B. E. A. Saleh, and M. C. Teich, "Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state," Phys. Rev. A 57, 3972-3986 (1998).
[CrossRef]

Vrijen, R. B.

E. Yablonovitch and R. B. Vrijen, "Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure," Opt. Eng. 38, 334-338 (1999).
[CrossRef]

Westbrook, P. S.

Wielandy, S.

Wiersma, D. A.

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Xu, C.

Yablonovitch, E.

D. V. Korobkin and E. Yablonovitch, "Two-fold spatial resolution enhancement by two-photon exposure of photographic film," Opt. Eng. 41, 1729-17322002).
[CrossRef]

E. Yablonovitch and R. B. Vrijen, "Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure," Opt. Eng. 38, 334-338 (1999).
[CrossRef]

J. Mod. Opt. (3)

R. W. Boyd and S. J. Bentley, "Recent progress in quantum and nonlinear optical lithography," J. Mod. Opt. 53, 713-718 (2006).
[CrossRef]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Parametric downconversion vs optical parametric amplification: a comparison of their quantum statistics," J. Mod. Opt. 49, 529-537 (2002).
[CrossRef]

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, "Implementation of sub-Rayleigh lithography using an N-photon absorber," J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

Opt. Eng. (2)

E. Yablonovitch and R. B. Vrijen, "Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure," Opt. Eng. 38, 334-338 (1999).
[CrossRef]

D. V. Korobkin and E. Yablonovitch, "Two-fold spatial resolution enhancement by two-photon exposure of photographic film," Opt. Eng. 41, 1729-17322002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (3)

J. Javanainen and P. L. Gould, "Linear intensity dependence of a two-photon transition rate," Phys. Rev. A 41, 5088-5091 (1990).
[CrossRef] [PubMed]

J. Perina, B. E. A. Saleh, and M. C. Teich, "Multiphoton absorption cross section and virtual-state spectroscopy for the entangled n-photon state," Phys. Rev. A 57, 3972-3986 (1998).
[CrossRef]

E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, "Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers," Phys. Rev. A 64, 043802 (2001).
[CrossRef]

Phys. Rev. Lett. (7)

J. Gea-Banacloche, "Two-photon absorption of nonclassical light," Phys. Rev. Lett. 62, 1603-1606 (1989).
[CrossRef] [PubMed]

G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, "Comment on 'Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,"' Phys. Rev. Lett. 86, 1389-1389 (2001).
[CrossRef] [PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

M. D'Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

N. P. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, "Nonclassical excitation for atoms in a squeezed vacuum," Phys. Rev. Lett. 75, 3426-3429 (1995).
[CrossRef] [PubMed]

B. Dayan, A. Peer, A. A. Friesem, and Y. Silberberg, "Nonlinear interactions with an ultrahigh flux of broadband entangled photons," Phys. Rev. Lett. 94, 043602 (2005).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the quantum lithography architecture.

Fig. 2
Fig. 2

(a) Two-photon excitation rate for the fringe maxima and minima plotted as functions of the intensity in each of modes a ̂ 2 and b ̂ 2 . The dashed and dotted curves show respectively the linear and quadraic contributions to the excitation rate for the fringe maxima. (b) Same as (a), but plotted as functions of the OPA gain G.

Fig. 3
Fig. 3

Fringe visibility V ( N ) plotted as a function of the gain G for various values of the order N of the multiphoton absorption process.

Fig. 4
Fig. 4

Absorption rate R ( N ) plotted as a function of the classical phase shift χ for a gain of G = 0.1 .

Fig. 5
Fig. 5

Absorption rate R ( N ) plotted as a function of the classical phase shift χ for a gain of G = 0.5 .

Fig. 6
Fig. 6

Absorption rate R ( N ) plotted as a function of the classical phase shift χ for a gain of G = 1.0 .

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

a ̂ 1 = U a ̂ 0 + V b ̂ 0 ,
b ̂ 1 = U b ̂ 0 + V a ̂ 0 .
U = cosh G ,
V = i exp ( i φ ) sinh G ,
a ̂ 2 = 1 2 [ a ̂ 1 + i b ̂ 1 ] ,
b ̂ 2 = 1 2 [ i a ̂ 1 b ̂ 1 ] .
a ̂ 2 = 1 2 [ ( U a ̂ 0 + V b ̂ 0 ) i ( U b ̂ 0 + V a ̂ 0 ) ] ,
b ̂ 2 = 1 2 [ i ( U a ̂ 0 + V b ̂ 0 ) + ( U b ̂ 0 + V a ̂ 0 ) ] .
I = a ̂ 2 a ̂ 2 = b ̂ 2 b ̂ 2 = V 2 = sinh 2 G ,
a ̂ 3 = 1 2 [ ( e i χ + i ) ( U a ̂ 0 + V b ̂ 0 ) + ( i e i χ 1 ) ( U b ̂ 0 + V a ̂ 0 ) ] ,
R ( 2 ) = σ ( 2 ) a ̂ 3 a ̂ 3 a ̂ 3 a ̂ 3 ,
a ̂ 3 a ̂ 3 a ̂ 3 a ̂ 3 = 4 V 2 [ U 2 cos 2 χ + 2 V 2 ] .
R min ( 2 ) = 8 σ ( 2 ) V 4 = 8 σ ( 2 ) sinh 4 G = 8 σ ( 2 ) I 2 .
R max ( 2 ) = 4 σ ( 2 ) V 2 [ U 2 + 2 V 2 ] = 4 σ ( 2 ) sinh 2 G [ cosh 2 G + 2 sinh 2 G ] = 4 σ ( 2 ) ( I + 3 I 2 ) .
R ( N ) = σ ( N ) a ̂ 3 N a ̂ 3 N ,
a ̂ 3 N a ̂ 3 N = n = 0 N 2 2 N 2 n P N 2 n N 2 V 2 ( N n ) U 2 n cos 2 n χ ,
P N N = N ! ,
P N 2 n N = 2 ( N 2 n + 1 ) P N 2 n + 1 N 1 + ( N 2 n ) P N 2 n 1 N 1 , where n = 0 , 1 , , N 2 .
R ( 2 ) = σ ( 2 ) a ̂ 3 2 a ̂ 3 2 = σ ( 2 ) 4 V 2 ( 2 V 2 + U 2 cos 2 χ ) ,
R ( 3 ) = σ ( 3 ) a ̂ 3 3 a ̂ 3 3 = σ ( 3 ) 24 V 4 ( 2 V 2 + 3 U 2 cos 2 χ ) ,
R ( 4 ) = σ ( 4 ) a ̂ 3 4 a ̂ 3 4 = σ ( 4 ) 48 V 4 ( 8 V 4 + 24 V 2 U 2 cos 2 χ + 3 U 4 cos 4 χ ) ,
R ( 5 ) = σ ( 5 ) a ̂ 3 5 a ̂ 3 5 = σ ( 5 ) 480 V 6 ( 8 V 4 + 40 V 2 U 2 cos 2 χ + 15 U 4 cos 4 χ ) .
V ( N ) = R max ( N ) R min ( N ) R max ( N ) + R min ( N ) ,

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